Separating Gas-Giant and Ice-Giant Planets by Halting Pebble Accretion
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A&A 572, A35 (2014) Astronomy DOI: 10.1051/0004-6361/201423814 & c ESO 2014 Astrophysics Separating gas-giant and ice-giant planets by halting pebble accretion M. Lambrechts1, A. Johansen1, and A. Morbidelli2 1 Lund Observatory, Department of Astronomy and Theoretical Physics, Lund University, Box 43, 22100 Lund, Sweden e-mail: [email protected] 2 Dep. Lagrange, UNSA, CNRS, OCA, Nice, France Received 15 March 2014 / Accepted 25 August 2014 ABSTRACT In the solar system giant planets come in two flavours: gas giants (Jupiter and Saturn) with massive gas envelopes, and ice giants (Uranus and Neptune) with much thinner envelopes around their cores. It is poorly understood how these two classes of planets formed. High solid accretion rates, necessary to form the cores of giant planets within the life-time of protoplanetary discs, heat the envelope and prevent rapid gas contraction onto the core, unless accretion is halted. We find that, in fact, accretion of pebbles (∼cm sized particles) is self-limiting: when a core becomes massive enough it carves a gap in the pebble disc. This halt in pebble accretion subsequently triggers the rapid collapse of the super-critical gas envelope. Unlike gas giants, ice giants do not reach this threshold mass and can only bind low-mass envelopes that are highly enriched by water vapour from sublimated icy pebbles. This offers an explanation for the compositional difference between gas giants and ice giants in the solar system. Furthermore, unlike planetesimal-driven accretion scenarios, our model allows core formation and envelope attraction within disc life-times, provided that solids in protoplanetary discs are predominantly made up of pebbles. Our results imply that the outer regions of planetary systems, where the mass required to halt pebble accretion is large, are dominated by ice giants and that gas-giant exoplanets in wide orbits are enriched by more than 50 Earth masses of solids. Key words. planets and satellites: formation – planets and satellites: gaseous planets – planets and satellites: composition – planets and satellites: interiors – protoplanetary disks 1. Introduction by a factor of 10, Kobayashi et al. 2011) have been proposed in order to form the cores of the giant planets. For the gas giants, In the core accretion scenario (Pollack et al. 1996), giant plan- planetesimal accretion is then halted artificially, or the opacity ets form by attracting a gaseous envelope onto a core of rock in the envelope is lowered, in order to reduce the envelope at- and ice. This theory is supported by the large amount of heavy traction timescale (Hubickyj et al. 2005). The ice giants are en- elements – elements with atomic number above He – found in visioned to remain small, because the protoplanetary gas disc the giant planets in our solar system (Guillot 2005). Additional dissipates during slow envelope growth (Pollack et al. 1996; evidence is provided by the observed dependence of giant exo- Dodson-Robinson & Bodenheimer 2010). planet occurrence on the host star metallicity, which is a proxy In this paper, we investigate the attraction of the gaseous for the dust mass enrichment of the protoplanetary disc (Fischer envelope when growth occurs by the accretion of pebbles, & Valenti 2005; Buchhave et al. 2012). as opposed to planetesimals. Pebble accretion rates are suffi- However, from a theoretical perspective it is poorly under- ciently high to form the cores of giant planets in less than stood how the core accretion scenario could have taken place, if 1 million years, even in wide orbits (Lambrechts & Johansen the cores grew by accretion of km-sized planetesimals and their 2012). Previous studies (Johansen & Lacerda 2010; Ormel & fragments. Protoplanetary disc life-times range from ∼3 Myr Klahr 2010; Bromley & Kenyon 2011; Lambrechts & Johansen (Haisch et al. 2001; Soderblom et al. 2013) to possibly as long 2012; Morbidelli & Nesvorny 2012) demonstrate that this is the as ∼6 Myr (Bell et al. 2013). This is much shorter than the time result of gas drag operating on pebbles, which dramatically in- needed to grow cores to completion in numerical simulations creases the accretion cross section (Sect. 2). The rapid accretion (Levison et al. 2010) of discs with solid surface densities com- of pebbles leads to high accretion luminosities that support a parable to the minimum mass solar nebula (MMSN, Hayashi growing gaseous envelope around the core (Sect. 3). We pro- 1981). Additionally, the gaseous envelope grows only slowly ceed by calculating the critical core mass, the lowest mass for on Myr timescales, because of the continued heating by accre- which a core can no longer sustain the hydrostatic balance of the tion of remnant planetesimals, even after clearing most of its proto-envelope. The critical core masses we find are of the order feeding zone (Pollack et al. 1996; Ikoma et al. 2000). Therefore, of ≈100 Earth masses (ME), too large compared to the inferred planets with gaseous envelopes are difficult to form by planetes- core masses of the gas giants in the solar system. Fortunately, imal growth within ∼10 Myr, especially outside the current orbit we find that there is a threshold mass already around 20 ME, of Jupiter (5 AU), where core growth timescales rapidly increase where the core perturbs the gas disc and halts the accretion of (Dodson-Robinson et al. 2009). pebbles, which initiates the collapse of the envelope before the As a result, protoplanetary discs with strongly enhanced critical core mass is reached (Sect. 4). This threshold mass is solid surface densities in planetesimals (exceeding the MMSN reached by the cores of the gas giants, but not by the ice giants in Article published by EDP Sciences A35, page 1 of 12 A&A 572, A35 (2014) wider orbits. By combining our calculations of the pebble isola- 10−2 tion mass and the critical core mass as a function of the envelope 80% 60% 40% 20% 0% enrichment, we can make estimates of the bulk heavy element 10−3 content of the giant planets. We find a good agreement with the composition of the giant planets in the solar system (Sect. 5). 10−4 We also discuss the implications of our model on the occurrence 5AU ⋅ and composition of giant exoplanets (Sect. 6). Finally, we briefly Mpeb summarize our work (Sect. 7). 10−5 30AU 5AU /yr) E 2. Pebble accretion /(M −6 ⋅ 10 M ⋅ 30AU The pebble accretion scenario, as outlined in Lambrechts & Mplan Johansen(2012), starts with the growth of pebbles from the 10−7 initial grains embedded in the protoplanetary disc (with sizes ≈µm) by collisions (Birnstiel et al. 2012) or through sublima- −8 τ <τ 10 τacc τdisc tion and condensation cycles around ice lines (Ros & Johansen acc> disc 2013). A fraction of the population of pebbles that drift towards the host star form dense swarms that subsequently collapse un- 10−9 der self-gravity to create planetesimals 100−1000 km in size. 10−1 100 101 102 103 M Such concentrations can occur through the streaming instability, c/ME driven by the mutual drag between particles and gas (Youdin & Goodman 2005; Youdin & Johansen 2007; Johansen & Youdin Fig. 1. Pebble accretion rates (red), planetesimal accretion rates (grey), 2007), or for example through the presence of vortices (Barge and minimal accretion rates required to sustain a stable gas envelope & Sommeria 1995) or pressure bumps (Whipple 1972). A more (black), as a function of the core mass. The curves for the minimal ac- cretion rates are nearly independent of orbital radius between 5−30 AU, detailed discussion can be found in the reviews by Chiang & but depend strongly on the opacity (Appendix B.3) and on the level of Youdin(2010) and Johansen et al.(2014). Finally, the largest envelope pollution by sublimation of icy pebbles. Labels at the top of planetesimals can act as the seeds of the planetary cores which the figure indicate H2O pollution of the atmosphere as a percentage with grow by rapidly sweeping up the remaining pebbles (Lambrechts respect to pure H/He nebular gas, corresponding to the fraction 1 − β & Johansen 2012). from Eq. (11). The critical core mass to collapse the gas envelope can We consider here cores that grow predominantly by the ac- be found at the intersection of an accretion curve with a critical curve. cretion of particles with radii of approximately mm-cm. Particle Accretion rate curves that fall in the yellow dashed region are too slow sizes can be expressed as a function of the gas drag timescale (t ) to form the cores of the giant planets before the dissipation of the gas f ˙ and Keplerian frequency Ω in terms of the Stokes number disc (τacc = Mc=Mc > τdisc = 2 Myr). Red circles mark the mass above K which pebble accretion is halted (Eq. (12)) and the gravitational col- ρ R lapse of the gas envelope is triggered. τ = Ω t = • ; (1) f K f ρH Here we have taken for simplicity an MMSN model with a par- where ρ• is the solid density, R the particle radius, ρ the midplane p gas density, and H the local gas scale height of the disc. Small ticle scale height given by Hp=H = αt/τ (Youdin & Lithwick dust particles (τ 1) are thus strongly coupled and comoving 2007), where αt is the turbulent diffusion parameter. Low parti- f cle scale heights are expected in dead-zones and discs where an- with the gas, while much larger objects (τf 1) are only weakly affected by gas drag. In the outer parts of the MMSN, in the gular momentum transport occurs primarily through disc winds region with semi-major axis a between 5 and 30 AU, particle (Turner et al.